DVI supports resolutions of up to 2560x1600.
HDMI theoretically supports resolutions of up to 2560x1600, but usually video card manufacturers limit the resolution to a maximum of 1920x1080 (unless you hook up a special hdmi to dvi adapter or you hack the graphics card firmware)
For high res gaming above 1920x1080, your best choice is DVI. If you're just playing at 1080p or below, then there is no difference.